Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
int main() {
  long long n;
  while (~scanf("%lld", &n)) {
    long long i, A, B, p = 0;
    for (i = 1; i < sqrt(2 * n); i++) {
      A = i * (i + 1) / 2;
      long long l = i, r = sqrt(2 * n), m = (l + r) / 2;
      while (l <= r) {
        B = m * (m + 1) / 2;
        if (A + B < n) {
          l = m + 1;
          m = (l + r) / 2;
        } else if (A + B > n) {
          r = m - 1;
          m = (l + r) / 2;
        } else {
          p = 1;
          break;
        }
      }
      if (p == 1) break;
    }
    if (p == 1)
      printf("YES\n");
    else
      printf("NO\n");
  }
  return 0;
}